How can I track a moving board and superimpose a video on top of it?
What you want is called Plane Tracking. The idea is that you associate 4 trackers to the vertices of a plane or an image.
Track the elements and select Create Plane Track.

In the compositor you use the tracking information to deform an image.
For more detail read the following links:
Can&#39;t choose Plane Track in Plane Track Deform node while compositing
Is it possible to take a mask clip and &#39;connect&#39; it to a specific point on a moving object?
And yes, it would be easier to use a green (or blue) screen on the card you film, otherwise you will need to create masks over the fingers and other elements that occlude the card. Such process is called rotoscoping, it is more complicated and tedious than dealing with green screen.